Velocity vs Relative Velocity
Velocity and relative velocity are both measurements of how fast an object is moving. Both velocity and relative velocity are really important concept in the fields like engineering, mechanics, rocket science, relativity and almost all the fields as far as physics and engineering are concerned. To get to know velocity and relative velocity much better we have to have a good understanding about frames. A frame is a system of coordinates defined in order to make measurements more convenient. There are two types of frames, Inertial frames and non-inertial frames. Inertial frames are defined as frames which are on rest or moving in a constant velocity. Non-inertial frames move in non-constant velocities (i.e. non-inertial frames accelerate). There are several types of coordinate systems, Cartesian coordinates, Spherical (polar) coordinates, cylindrical coordinates are to name a few. Velocity and relative velocity also have different characteristics when it comes to classical mechanics and relativistic mechanics.
Velocity is defined as the rate of change of distance. Mathematically speaking velocity equals dx/dt (read as d, dt x) according to the theories of calculus. It is also denoted in ẋ. Velocity also takes the form of angular velocity; in that case velocity is equal to the rate change of angle. Both linear velocity and angular velocity are vectors. Linear velocity has the direction of instantaneous movement whilst the angular velocity has the direction which is decided by the corkscrew method. Velocity is a relativistic variant, which means the laws of relativity must be applied for velocities compatible with the speed of light.
Relative velocity is the velocity of an object relative to another object. In the vector form this is written as V̰A rel B = V̰A – V̰B. V̰rel is the velocity of an object “A” relative to object “B”. Usually a velocity triangle or a velocity parallelogram is used to calculate relative velocity between two objects. Velocity triangle theory states that if VA rel Earth and VEarth rel B are indicated in two sides of a triangle proportion to the magnitude and direction the third line indicates the direction and magnitude of the relative velocity. Relative velocity is a relativistic variant.
What is the difference between velocity and relative velocity?
Velocity and relative velocity are both measurements of the speed and the direction of a movement of an object. Velocity is measured by a still observer. A still observer must be placed on a still frame. But a still frame is just a concept. All our regular measurements are done on the earth. We know that earth is on an orbit around the sun. Being on an orbit means there’s always a centripetal acceleration towards the center of motion. This means earth is not an inertial frame. But for most of the calculations we take earth as a still frame. But in fact what we measure is the relative velocity of the object relative to the earth. The velocity is in fact a derivation of the relative velocity with VB being zero.